In 1986 the concept of a subsumption architecture for path planning and motion control of robots was developed. This concept provides a method for structuring motion from the bottom up using layered sets of rules. Later, the rules were represented as a network of probabilistic constraints linking the successive positions (poses) of a mobile robot. Currently, behavior-based approaches are practiced by a number of leading research institutions and companies, including MIT, Stanford, CMU, University of Arizona, Idaho National Labs and iRobot.
Further developments in path planning for obstacle avoidance were made by Paolo Fiorini and Dr. Zvi Shiller (P. Fiorini et al., International Journal of Robotics Research, 17(7): 760-772, July 1998). More particularly, Fiorini and Shiller developed an algorithm having decreased computational intensity (this was accomplished by forming the set RAV(ti) as a discrete grid). In accordance with the algorithm, a position of a node is determined based on an operator (e.g., velocity) that is multiplied by a chosen time interval. The position reached at the end of each maneuver is the successor of the function nj(ti). Further, the position of the node is determined for every operator in RAV such that a node is completely expanded when all operators obi in RAV(j) have been applied. By assigning an appropriate cost to each branch that the node may traverse, an appropriate objective function can be maximized/minimized to calculate trajectory.